Doing something like changing direction CAN help with what he is talking about because it helps the horse refocus on YOU, and NOT what he is spooking at, so he learns to focus on you, rather than his surroundings, the more you mentally occupy his mind, especially from the beginning.
It can also keep them light on the front end too. Do a lot of turning and other work to keep horses light on the front end when stopping.
I too do all three gaits within the first few rides...not forever, mind you, but I don't putz around, I can refine later, but I like to know that they will do it for me from the beginning. It also helps with resale, if that's the case, and if they are being trained for someone, I can't wait until the last 5 days to know the horse will canter...he should already know his leads when I send him home.